a) Field of the Invention
This invention relates to a method of and apparatus for determining the state of polarisation of a pencil of electromagnetic radiation. In particular, though not exclusively, the invention relates to such a method of and apparatus for determining the state of polarisation of an incoming pencil of electromagnetic radiation in or closely adjacent the visible spectrum.
b) Description of the Prior Art
The state of polarisation of an electromagnetic wave may be represented by a polarisation ellipse, the limiting states of which are when the ellipse degenerates into a straight line, or into a circle. In these two limiting cases, the wave is described as being linearly polarised or circularly polarised, as appropriate. The state of polarisation of a wave may be described by four parameters S.sub.0, S.sub.1, S.sub.2 and S.sub.3 known as the Stokes parameters. The parameter S.sub.0 is proportional to the intensity of the wave, whereas the parameters S.sub.1, S.sub.2 and S.sub.3 are related in a simple way to the angle which specifies the orientation of the polarisation ellipse, and also to the angle which characterises the ellipticity and the sense in which the ellipse is being described. An alternative representation for the polarisation of a wave is the Poincare sphere, and in this case the parameter S.sub.0 represents the radius of the sphere and the parameters S.sub.1, S.sub.2 and S.sub.3 are the Cartesian co-ordinates of a point P on the sphere which uniquely describes the state of polarisation of the wave.
The four Stokes parameters are not totally independent of each other, but are related to each other by the relationship EQU S.sub.0.sup.2 =S.sub.1.sup.2 +S.sub.2.sup.2 +S.sub.3.sup.2
Therefore experimentally to determine the state of polarisation of a wave, a minimum of three measurements need to be performed on the wave to obtain characteristics from which the four Stokes parameters can be deduced. In practice, however, it is usual to make four measurements as this provides a consistency check on the measurements through the above relationship between the Stokes parameters. There have been various proposals for methods and apparatus to fulfil this objective. Such methods and apparatus have been described for example in "Survey of Methods for the Complete Determination of a State of Polarisation" by P. S. Hague, published in SPIE Volume 88, page 3-10, 1976 and all currently-available apparatus operates on one of the several methods described in that paper. Despite the age of that paper, it still represents the state of the art so far as the fundamental operating methods are concerned, though the various apparatuses described have of course since then been improved.
Each of the methods described in the paper by Hague has disadvantages, the significance of which depends upon the use to which apparatus operating on that method is put. The technique of using an adjustable retarder and analyser ("Method 1" in Hague's paper) requires the presence of a wave the polarisation of which remains substantially constant for a relatively long period of time, in order to allow the four measurements to be performed sequentially on that wave, each of the four measurements requiring the angular orientation of the retarder or the analyser, or both, to be reset. This puts up a limit on the minimum possible sampling time of the order of several tens of seconds, needed to complete the required four measurements and so to obtain an accurate assessment of the state of polarisation of the wave.
The use of a rotating element polarimeter ("Method 2" in Hague's paper), allows very much faster measurements to be performed. By continuously rotating a quarter-wave plate in the optical axis, it is possible to perform spectral analysis on an electrical signal produced by an optical detector, which analysis is timed to the plate rotation. In this way, a sampling time of the order of one second can be obtained. More recently, there have been proposals for electro-optic simulations of rotating quarter-wave plates, where a suitable crystal for example of lithium-niobate has two orthogonal pairs of electrodes deposited across it, which are electronically driven in quadrature. With sampling the optical detector output at relatively high rates a band width of up to about 150 Hz has been obtained for such a system.
With the advent of optical fibre communication systems, the determination of the state of polarisation of a wave has become most important. The next generation of such communication systems will use coherent detection in homodyne or heterodyne form, for example to enhance receiver sensitivity and to allow tightly-packed wavelength-division multiplexing. If this is to be achieved, it is necessary to match the polarisation states of the signal and local oscillator waves, at the optical detector.
Experience shows that if a well-defined linearly-polarised wave is fed from a transmitter into a `real` long optical fibre cable, the polarisation state of the wave emerging from the cable fluctuates randomly. This in effect constitutes polarisation noise which is associated with the received optical signal, and this leads to a need for a polarisation controlling device as a part of a polarisation tracking loop, to enable the local oscillator polarisation to be continually changed so as to keep the latter precisely matched to the fluctuating polarisation state of the received optical signal.
There is thus a need for a polarimeter able to determine accurately and quickly the polarisation state of a relatively small beam of light, on the one hand to enable the development of suitable polarisation controllers, and on the other to characterise the polarisation noise associated with optical fibre communication systems.
A basic method for determining the state of polarisation of a wave is to perform a minimum of three, but in practice usually four, separate transmitted intensity measurements on the wave, each time using a different `filter` arrangement in the optical path of the wave to the intensity detector. Such a set of `filters`, allowing the derivation of the Stokes parameters merely from light intensity measurements following the passage of the light therethrough, will hereinafter be referred to as a set of "Stokes filters". An example of a set of "Stokes filters", as defined just above, comprises a first `filter` totally insensitive to polarisation but having a 50% transmission factor, though this filter could have other transmissivities (up to 100%--e.g. a clear aperture) provided appropriate corrections are then applied in the subsequent analysis of the polarisation state. The second and third filters are linear polarisers with their transmission axes at 45.degree. to each other, and the fourth filter is a circular polariser, being a combination of a linear polarizer and a phase retardation plate, and opaque to left-handed circular polarised light.
It should be emphasised that the example of a particular set of filters as described above represents only one of an infinite number of possible sets of filters which could fulfil the definition of a set of `Stokes filters` given above.
A set of Stokes filters, as described above, may be used to attempt to determine the state of polarisation of a beam of light issuing from a fibre optic cable. However preliminary trials have shown that the polarisation noise spectrum of such a beam might extend from DC up to perhaps 2 or 3 kHz, which is well beyond the measuring capability of known forms of polarimeter using a set of Stokes filters and constructed in accordance with the teachings of Hague. Though theoretically a system employing a set of Stokes filters including an electronic simulation of a quarterwave plate could perhaps achieve a measurement bandwidth of about 8 kHz, such a polarimeter would be extremely expensive to construct and could really be regarded only as a piece of laboratory equipment; it would not be practical to construct such a polarimeter as a commercial, robust, easy-to-use and automatic polarimeter, both for static and dynamic measurements.